PPT-Riemann sums, the definite integral, integral as area

Section 52a First we need a reminder of sigma notation How do we evaluate and what happens if an infinity symbol appears above the sigma The terms go on indefinitely. adding it all up. Integral Calculus. 1. Goal. Compute the . signed. area . under some portion of an arbitrary curve. Integral Calculus. 2. Divide and Conquer. Integral Calculus. 3. Animatedly. Integral Calculus. Sigma Notation. What does the following notation mean?. means. the sum of the numbers from the lower number to the top number.. Area under curves. In 5.1, we found that we can approximate areas using rectangles.. Ms. . Battaglia. – . ap. calculus . Definite integral. A definite integral is an integral . with upper and lower bounds. The number a is the . lower limit. of integration, and the number b is the . Antiderivative. First let’s talk about what the integral means!. Can you list some interpretations of the definite integral?. Here’s a few facts. :. 1. If f(x) > 0, then returns the . numerical value of the area between. Riemann Sums. -Left, Right, Midpoint, Trapezoid. Summations. Definite Integration. We want to think about the region contained by a function, the x-axis, and two vertical lines x=a and x=b. . a. Antidifferentiation. Section 5.3a. Consider the “Do Now”…. What happens to an integral value if we simply . switch. t. he order . of the limits of integration???. If we sum rectangles moving from . FACULTY OF EDUCATION. Mathematics Education Department. Integratıon, fınıte sum and defınıte ıntegral. 1. Orhan TUĞ (PhDc). A. Figure 5.1.8. Figure 5.1.9. Error analysis. Error analysis. Upper and lower estimates of the area. Calculus. Calculus answers two very important questions.. The first, how to find the instantaneous rate of change, we answered with our study of derivatives. The second we are now ready to answer, how to find the area of irregular regions.. Rizzi – . Calc. BC. The Great Gorilla Jump. The Great Gorilla Jump. Left-Hand Riemann Sum. Right-Hand Riemann Sum. Over/Under Estimates. Riemann Sums Summary. Way to look at accumulated rates of change over an interval. Area and Estimating with Finite Sums. Section 5.2. Sigma Notation and Limits of Finite Sums. Section 5.3. The Definite Integral. Section 5.4. The Fundamental Theorem of Calculus. As the number of rectangles increased, the approximation of the area under the curve approaches a value.. Copyright .  2010 Pearson Education, Inc.. Section 5.3 – The Definite Integral. Definition. Riemann Sums. The sums you studied in the last section are called . Riemann Sums. When studying . area under a curve. , we consider only intervals over which the function has positive values because area must be positive. Riemann Sums. a. b. The rectangles need not have equal width, and the height may be . any. value of . f. (. x. ). within the subinterval. .. 1. Partition (divide) [. a,b. ] into . N. subintervals.. COURSE name : - INTEGRAL CALCULUS . DEPARTMENT OF MATHEMATICS . COURSE CODE :- MATH 309 TH . Course Description. Theorem 1: On Definite Integral . Theorem 2 : On Definite Integral. . Theorem 3 : On Definite Integral.